Dec 6 (Reuters) - Around 300 Islamists took to the streets of the Libyan port of Benghazi on Friday demanding the fall of the government and an end to strikes and sit-ins stopping crude exports - the first sign of public opposition to the blockades in the oil-rich east.

A regional autonomy movement has seized the country's two biggest ports in Es-Sider and Ras Lanuf, both of them in eastern Libya, the source of 60 percent of the OPEC producer's oil wealth.

Other groups demanding a greater share of oil wealth and other rights have halted exports at Hariga port in Tobruk in the far east.

The actions have devastated Libya's oil trade, the main source of revenue and hard currency in a country still struggling with turmoil two years after the overthrow of Muammar Gaddafi.

"We demand the liberation of oil exports," read a banner held up by Islamists gathered in Libya's second-largest city where gunshots and car bombs occur almost daily.

Ismail Salabi, a prominent Islamist militia leader, accused the strikers of devastating the economy. "We have many demands but the most important is to lift the port seizures," he said.

Groups occupying oil sites are mainly made up of former fighters and other militias who helped overthrow Gaddafi.

Many in the east sympathise with their goals but the public mood has soured in the past few days with power cuts in Benghazi and other cities blamed by the government on a sharp fall in oil and gas production.

The Islamists called for the overthrow of Libya's interim government, led by Prime Minister Ali Zeidan, accusing it of being incompetent and too liberal.

They also held up banners demanding the establishment of an Islamic state with strict application of Islamic law, or sharia, and the dissolution of all political parties.

Libya has seen fierce debate over the role of Islam in its new democracy with the rise of Islamists long suppressed by Gaddafi.

The Islamists in Benghazi on Friday said they were not linked to the hardline movement Ansar al-Sharia, blamed for the 2012 attack on the U.S. consulate in the city.

Libya's National assembly on Wednesday voted through a statement that Islamic law should be the source of all legislation, in an apparent bid to outflank the hardline Islamists. Officials said the statement showed the assembly's intent, but was not in itself binding legislation.

Libya currently produces 224,000 barrels of oil a day, a fraction of the 1.4 million it was pumping out in July when the strikes and sit-ins first erupted, the deputy oil minister told Reuters on Monday.

On Thursday, members of the Amazigh minority living in western Libya said they had ended a blockage of a gas pipeline feeding a power plant, bowing to rising public pressure.

The Amazigh, or Berber, want the use of their language to be guaranteed by the constitution. (Reporting by Ayman al-Warfalli and Feras Boslaum; Writing by Ulf Laessing; Editing by Andrew Heavens)